Computing the strong L_p− Nash equilibrium for Markov chains games: Convergence and uniqueness

This paper presents a novel method for computing the strong L_p− Nash equilibrium in case of a metric state space for a class of time-discrete ergodic controllable Markov chains games. We first present a general solution for the L_p- norm for computing the strong L_p− Nash equilibrium and then, we suggest an explicit solution involving the norms L₁, L₂ and L_∞. For solving the problem we use the extraproximal method. We employ the Tikhonov's regularization method to ensure the convergence of the cost-functions to a unique equilibrium point. We prove that the proposed method convergence in exponential time to a unique strong L_p− Nash equilibrium. A game theory example illustrates the main results.